2024/10/09 by Helton Leal, Leal, Helton, Matheus Vieira +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2410.07372
openalex publication_date 2024/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the spectrum of the drift Laplacian on Ricci expanders. We show that the spectrum is discrete when the potential function is proper, and we show that the hypothesis on the properness of the potential function cannot be removed. We also extend previous results concerning the asymptotic behavior of the potential function on Ricci expanders. This allows us to conclude that the drift Laplacian has discrete spectrum on Ricci expanders whose Ricci curvature is bounded below by a suitable constant, possibly negative. Further, we compute all the eigenvalues of the drift Laplacian on rigid expanders and rigid shrinkers. Lastly, we investigate the second eigenvalue of the drift Laplacian on rigid Ricci expanders whose Einstein factor is a closed hyperbolic Riemann surface.